At what common Celsius temperature is the rms velocity of oxygen molecules (molar mass = 32 g/mol)double that of hydrogen molecules (molar mass = 2.0 g/mol)?
A)-50
B)zero
C)no such temperature exists
D)2.0
E)16

Question

Quizplus · Accepted Answer

The root-mean-square (rms) velocity of a gas molecule is given by the formula $v_{rms} = \sqrt{\frac{3kT}{m}}$, where $k$ is the Boltzmann constant, $T$ is the temperature in Kelvin, and $m$ is the mass of a molecule. For the rms velocity of oxygen to be double that of hydrogen, the equation $2\sqrt{\frac{3kT}{m_{H_2}}} = \sqrt{\frac{3kT}{m_{O_2}}}$ would have to be satisfied. However, when you solve for $T$, you find that the temperature depends on the ratio of the masses of the molecules, and since the masses are constants, there is no temperature at which the rms velocity of oxygen is exactly double that of hydrogen due to the square root dependence on mass. This means no such temperature exists where this condition is met exactly.

At What Common Celsius Temperature Is the Rms Velocity of Oxygen